ABC is an isosceles right angled triangle with ∠ABC = 90˚. A semi-circle is drawn with AC as the diameter. … of the shaded region….
Answers:
In △ABC,
AC2 = AB2 + BC2
= 72 + 72
= 49 + 49
= 98
⇒ AC = √98
= 7√2 cm
Radius of semi circle = 7√2/2 cm
∴ Area of shaded region = (Area of semi-circle) – Area of △ABC
= ½(πr2) – ½ × base × height
= ½ π (7√2/2)2 – ½ × 7 ×7
= ½ × 22/7 × (49 × 2)/4 – ½ × 49
= 77/2 – 49/2 = 28/2 = 14 cm2